syr2(3F)

NAME
     SSYR2, DSYR2 - Performs symmetric rank 2 update of a real symmetric
     matrix

SYNOPSIS
     Real

        CALL SSYR2 (uplo, n, alpha, x, incx, y, incy, a, lda)

     Double precision

        CALL DSYR2 (uplo, n, alpha, x, incx, y, incy, a, lda)

DESCRIPTION
     These routines perform the following symmetric rank 2 operation:

          A <- alpha xyT + alpha yxT + A

     where alpha is a real scalar, yT is the transpose of y, xT is the
     transpose of x, x and y are n-element vectors, and A is an n-by-n real
     symmetric matrix.

     This routine has the following arguments:

     uplo      Character*1.  (input)
               Specifies whether the upper or lower triangular part of
               matrix A is being supplied, as follows:

               uplo= 'U' or 'u':  only the upper triangular part of array a
               is referenced.
               uplo= 'L' or 'l':  only the lower triangular part of array a
               is referenced.

     n         Integer.  (input)
               Specifies the order of matrix A.  n >= 0.

     alpha     Scalar alpha.  (input)
               SSYR2: Real.
               DSYR2: Double precision.

     x         Array of dimension 1+(n-1) * |incx|.  (input)
               SSYR2: Real array.
               DSYR2: Double precision array.

     incx      Integer.  (input)
               On entry, incx specifies the increment for the elements of
               x.  incx must not be 0.

     y         Array of dimension 1+(n-1) * |incy|.  (input)
               SSYR2: Real array.
               DSYR2: Double precision array.

     incy      Integer.  (input)
               On entry, incy specifies the increment for the elements of
               y.  incy must not be 0.

     a         Array of dimension (lda,n).  (input and output)
               SSYR2: Real array.
               DSYR2: Double precision array.

               Before entry with  uplo='U' or 'u', the leading n-by-n upper
               triangular part of array a must contain the upper triangular
               part of the symmetric matrix and the strictly lower
               triangular part of a is not referenced.  On exit, the upper
               triangular part of the updated matrix overwrites the upper
               triangular part of array a.

               Before entry with uplo='L' or 'l', the leading n-by-n lower
               triangular part of array a must contain the lower triangular
               part of the symmetric matrix and the strictly upper
               triangular part of a is not referenced.  On exit, the lower
               triangular part of the updated matrix overwrites the lower
               triangular part of array a.

     lda       Integer.  (input)
               Specifies the first dimension of a as declared in the
               calling program.  lda >= MAX(1,n).

NOTES
     SSYR2/DSYR2 is a Level 2 Basic Linear Algebra Subprogram (Level 2
     BLAS).

     When working backward (incx < 0 or incy < 0), this routine starts at
     the end of the vector and moves backward, as follows:

          x(1-incx * (n-1)), x(1-incx * (n-2)) , ..., x(1)

          y(1-incy * (n-1)), y(1-incy * (n-2)) , ..., y(1)

SEE ALSO
     HER2(3F)